Integer Smith Form via the Valence : Experience with large sparse matrices from Homology

28/08/00


Cliquez ici pour démarrer


Table des matières

Integer Smith Form via the Valence : Experience with large sparse matrices from Homology

Smith form of an integer matrix A ? Zm x n

Motivation

Our Problem : Homology matrices Algebraic topology of simple graphs

4 ? 4 chessboard complex : boundary map of size 96 ? 72 between dimensions 1 and 2 with AAT and ATA

Smith form computation : State of the art

Idea : work with powers of primes

Contents

Valence Smith Form of a matrix A

Integer Valence computation

Integer minimum polynomial

Degree of the minimum polynomial

How many primes to use ?

Valence Smith Form of a matrix A

Reducing the set L when using B = ATA

Valence Smith Form of a matrix A

Local Smith Form at p : via elimination

Local Smith form at p : Blackbox

Last invariant factor at p : q-adic

Valence Smith Form of a matrix A

Linbox and Athapascan Experiments with Homology matrices

Linbox project (NSF-CNRS) University of Delaware, North Carolina State University, University of Western Ontario, University of Calgary, Laboratoire LMC, Laboratoire ID.

Which interface ?

Athapascan -1 : Parallel Application Programming Interface

Parallel Valence

Parallel Valence algorithm

Homology Valence-only parallel computation

Diapositive PPT

Parallel Wiedemann

Diapositive PPT

Wiedemann algorithm on SMP

Ranks mod 65521 : Wiedemann versus Gauß

Sequential Integer Smith form

Prospects

Auteur:Jean-Guillaume Dumas

Messagerie: Jean-Guillaume.Dumas@imag.fr

Page d'accueil:

Télécharger la source de la présentation